Review question

# When does this inequality have a finite number of integer solutions? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6414

## Suggestion

Let $a$, $b$, $c$ be positive numbers. There are finitely many positive whole numbers $x$, $y$ which satisfy the inequality $a^x > cb^y$ if

1. $a>1$ or $b<1$.

2. $a<1$ or $b<1$.

3. $a<1$ and $b<1$.

4. $a<1$ and $b>1$.

It’s important to notice that the question refers to a finite number of solutions…

Can we use logarithms to rewrite the inequality?